Unit 1: Limits and Continuity (6 hrs)
Limit of a function, Indeterminate forms, Algebric properties of limit (without proof), Theorems on Limits of Algebraic and Transcendental Function, Continuity of a function, types of discontinuity. Exercises on evaluation of limits and test of continuity.(Mathematica)
Unit 2: Differentiation (6 hrs)
Ordered Pairs, Cartesian Product, Relation, Domain and Range of a Relation, Inverse of a Relation; Types of Relations: Reflective, Symmetric, Transitive, and Equivalence Relations. Definition of Function, Domain and Range of a Function, Inverse Function, Special Functions(Identity, Constant), Algebraic(Linear, Quadratic, Cubic), Trigonometric and Their Graphs. Definition of Exponential and Logarithmic functions, Composite Function.(Mathematica)
Unit 3: Application of Differentiation (8 hrs)
The derivatives and slope of the curve; Increasing and decreasing function; convexity of curves; maximization and minimization of a function; Differentiation and marginal analysis; price and output; Competitive equilibrium of firm, Illustrations. Drawing graphs of algebraic function by using first and second order derivatives.(Mathematica)
Unit 4: Integration and Its Applications (8 hrs)
Riemann Integral; Fundamental Theorem (Without Proof); Technique of Integration; Evaluation and Approximation of Definite Integrals; Improper Integrals; Application of Definite Integrals; Quadrate, Rectification; Volume and Surface Integral. Trapezoidal and Simpson's Rules of Numerical Integration.(Mathematica)
Unit 5: Differential Equations (7 hrs)
Differential Equation and its Order and Degree, Differential Equations of First Order and First Degree; Differential Equations with Separable Variables, Homogenous and Exact Differential Equations.
Unit 6: Computational Method (10 hrs)
Linear Programming Problem(LPP), Graphical Solution of LPP in two Variables, Solution of LPP by Simplex Method(up to 3 variables), Solution of System of Linear Equations by Gauss Elimination method, Gauss Seidel Method and Matrix Inversion Method, Bisection method, Newton-Raphson Method for Solving Non-Linear Equations.(Excel/Matlab)